Dengue fever mapping in Bangladesh: A spatial modeling approach

Abstract Background Epidemics of the dengue virus can trigger widespread morbidity and mortality along with no specific treatment. Examining the spatial autocorrelation and variability of dengue prevalence throughout Bangladesh's 64 districts was the focus of this study. Methods The spatial autocorrelation is evaluated with the help of Moran I and Geary C. Local Moran I was used to detect hotspots and cold spots, whereas local Getis Ord G was used to identify only spatial hotspots. The spatial heterogeneity has been detected using various conventional and spatial models, including the Poisson‐Gamma model, the Poisson‐Lognormal Model, the Conditional Autoregressive (CAR) model, the Convolution model, and the BYM2 model, respectively. These models are implemented using Gibbs sampling and other Bayesian hierarchical approaches to analyze the posterior distribution effectively, enabling inference within a Bayesian context. Results The study's findings show that Moran Iand Geary Canalysis provides a substantial clustering pattern of positive spatial autocorrelation of dengue fever (DF) rates between surrounding districts at a 90% confidence interval. The Local Indicators of Spatial Autocorrelation cluster mapped spatial clusters and outliers based on prevalence rates, while the local Getis‐Ord G displayed a thorough breakdown of high or low rates, omitting outliers. Although Chattogram had the most dengue cases (15,752), Khulna district had a higher prevalence rate (133.636) than Chattogram (104.796). The BYM2 model, determined to be well‐fitted based on the lowest Deviance Information Criterion value (527.340), explains a significant association between spatial heterogeneity and prevalence rates. Conclusion This research pinpoints the district with the highest prevalence rate for dengue and the neighboring districts that also have high risk, allowing government agencies and communities to take the necessary precautions to mollify the risk effect of DF.

The mosquito-borne dengue fever (DF) is the most quickly spreading disease worldwide. 1During an epidemic in 1870, the disease was known as "Denga" in Zanzibar, where the name "Dengue" first appeared. 2Classic DF, dengue hemorrhagic fever, and dengue shock syndrome are all caused by dengue virus (DENV), which is carried by day-biting Aedes mosquitoes, primarily Aedes aegypti and Aedes albopictus. 3About 2.5 billion people reside in dengue-endemic nations, with an annual estimated 50 million new dengue cases reported. 4As an example of a disease that could constitute a public health emergency of international concern with implications for health security due to disruption and rapid epidemic spread beyond national borders, DF is mentioned in World Health Assembly resolution WHA58.3 from 2005, which discusses the revision of the International Health Regulations (IHR). 5,6re than 1.8 billion people (70% of the global population at risk) live in the WHO's Southeast Asia Region and Western Pacific Region, which are also responsible for more than 75% of the global sickness burden attributable to DF. 4 Since 2000, both the number of people infected and the area affected by the dengue epidemic have increased.In 1964, DF was first recorded in eight countries: Bangladesh, India, Indonesia, Maldives, Myanmar, Sri Lanka, Thailand, and Timor-Leste.Bhutan announced its first DF case in 2004.Nepal first reported locally-transmitted dengue cases in November 2006.
Only in the Democratic People's Republic of Korea have there been no reports of locally transmitted DENV.
In the late summer of 1964, a "Dacca Fever" outbreak in the capital city of Bangladesh (now Dhaka) led to the discovery of the country's first dengue disease. 7The country experienced intermittent dengue infections and brief outbreaks between 1964 and 1999, but they weren't formally documented. 8Since the disease first became widespread in 2000, when there were 5551 cases and 93 fatalities, it has become a serious hazard to the public's health throughout three large cities (Dhaka, Chittagong, and Khulna) and 17 towns, with a case fatality rate of 1.7%. 9The Ministry of Health and Family Welfare formed the CDC as a separate unit inside the DGHS's Disease Control Division in 2000, following a severe dengue outbreak in Dhaka city that year. 102][13] As of December 2014, the Directorate General of Health Services (DGHS) had received reports of over 28,000 illnesses and 242 deaths since January 2000. 14An increase in dengue outbreaks from 2769 in 2017 to 10,148 in 2018 has caused increased public concern. 15After notifying the country of a dengue outbreak in August of 2019, the number of reported cases has dropped from 430,282 in 2019 to 59,675 in 2020. 15DF is a serious problem in Bangladesh, with 28,429   confirmed cases in 2021 and more cases being recorded every day.
Data science is playing an increasingly crucial role in identifying and implementing solutions to social and economic problems because of the exponential growth in the available data and the continuous improvements in information technology. 167][18] The deadly global DF outbreak that began in 2019 has also increased the usage of data science in the healthcare industry. 191][22] Epidemiology can be thought of as the study of disease occurrence and transmission to identify risk factors.
Box-Jenkins was used in a study to develop an ARIMA model, which stands for autoregressive integrated moving average in 23 to anticipate changes in the prevalence of dengue.Dengue hemorrhagic datasets from several Mexican states and union territories were categorized using cluster analysis. 24The purpose of this study was to make government policy and monitoring processes better.While standard statistical models have been used to evaluate demographic factors relevant to dengue transmission in Bangladesh, 25  Disease distributions are mapped using parameter estimates derived from both observational data and prior assumptions using Bayesian inference. 26,27To create a dengue risk map, spatial and spatiotemporal modeling techniques are quite helpful. 27,28Overdispersion and spatial correlation in the data are typically modeled using hierarchical Bayesian approaches.Random effect models, such as the Poisson-Lognormal (PLN) and Poisson-Gamma distributions, are two common approaches to this issue. 28Data overdispersion due to Poisson errors, also known as "spatially uncorrelated heterogeneity" in disease mapping, is accounted for by these two models. 29erdispersion in Poisson data can arise due to spatially unstructured covariates, excessive zero counts, or counts that deviate significantly from the mean. 29To address these issues, two proposed models assume a gamma or lognormal distribution of random effects.The Conditional Autoregressive (CAR) model explores the spatial relationships between data and often performs better than models only correcting for unstructured heterogeneityusing weighting schemes. 29th unstructured and structured random effects coexist in Convolution (COV) models. 30,31The combined model accounts for both overdispersion and clustering through the use of gamma and normal random effects.
This study presents the results of our efforts to answer the following research topics through primary research.Does the clustering of the prevalence rate of a dengue outbreak suggest anything about the influence of the geographic features?How then do we quantify the data's geographical dependence and spatial heterogeneity?Furthermore, how can we include this in the statistical models?Do governments in a cluster look to the policies of their neighboring districts for guidance, or do they act independently?In Section 2, detailed explanations of methods and materials, including the Bayesian statistical models and sources of data, are presented.Using spatial autocorrelation and results from a suitable model, the primary contributors to the elevated prevalence rate of dengue in Bangladesh are identified in Section 3. Finally, Section 4 emphasized how the study's findings may provide government authorities with actionable information to lower the occurrence of dengue.

| Spatial data sources
The study area of this research is depicted in Figure 1.The data used in this article was obtained from the DGHS website (https://dghs.gov.bd/), which is publicly available.Data on the total number of afflicted patients were collected from this source beginning on January 01, 2022, and continuing through December 31, 2022.It is important to note that any personal information of individuals was not included in the data set.The other two variables, that is, the population of each district and the annual growth rate of the population by district, were taken from the census conducted by the Bangladesh Bureau of Statistics (BBS) (https://tinyurl.com/3dcspsfp) in 2011.The anticipated population of all 64 districts in 2022 was collected from (https://tinyurl.com/3j4ff8r4).Both the data sources are publicly available too.By using the geometric model, the predicted population growth rate is determined for 2022.Here is the formula for determining the rate of expansion: where P 0 is the 2011 population, Pis the anticipated 2022 population, n determines the time interval between two successive censuses, and r determine the annual growth rate for 2022.According to this study, the prevalence rate formula stands for:

No of Dengue Affected Cases Annual Growth Rate District Population
Prevalence rate = .× × 100, 000 The burden on the health and social care system at any given time can only be understood through a district-by-district prevalence rate evaluation; hence this must be carried out.After that, an estimated number of impacted people is computed per 100,000 in each district.

| Distribution of response variable
In terms of probability distributions, the Poisson distribution is discrete.To put it another way, the variable's value can only be a whole number, such as 0, 1, 2, 3, and so forth.Neither a decimal nor a fraction will do. 33Below is a representation of the probability mass function (pmf): here, e determines the Euler's number (e = 2.71828…), λ and y determine the incidence rate and the number of instances, respectively.

| Spatial autocorrelation
According to Getis, 34 the concept of spatial autocorrelation is one of the fundamental components of spatial analysis.It is useful for testing the hypothesis of systematic geographical variation by immediately considering the feature districts and their related values. 35Conventional models make the premise that observations are independent of one another; however, spatial correlation creates a divergence from that assumption. 36The spatial autocorrelation approach examines the geographical patterns of individual entities to determine whether they are clustered, random, or dispersed. 37This can be done by assessing whether or not the patterns are random, dispersed, or clustered.

| Moran's I autocorrelation
A correlation coefficient known as Moran's I can be used to evaluate the degree of spatial autocorrelation in data collection.In other words, it calculates an object's degree of similarity to its immediate surroundings. 38The observations are not independent if there is a correlation between the items.Clustering, dispersion, and randomness are the three patterns it can identify when given a set of features and an associated characteristic.Comparing variable states over time, assessing the degree of self-association in a given location, and determining its relationship to others are all facilitated by this tool.The values of Moran's I fluctuate between +1 and 1, where 39 Similar to Pearson's coefficient, 40 Moran'sI statistic has the following formula: In this research, n determines the total number of districts, ω ij is a quantification of the spatial weight of two districts i and j.The variables of interest are transformed into z-scores, and the numerator is the sum of the products of z-scores in neighboring districts.The first step in a spatial autocorrelation analysis is to create a spatial weight matrix that details the neighborhood structure for each site, as the weights are the row-standardized ∑ω ij .The term "adjacency" is used to describe neighboring administrative districts that exist close to a certain district.
Administrative districts are not considered significantly influential enough to one another if they are not next to one another. 38A positive spatial autocorrelation will result from the presence of two positively correlated districts with large scores.If, on the other hand, two districts emerge with lower scores, then this indicates negative Study area of this study (district-wise map of Bangladesh). 32patial autocorrelation. 41For this reason, a perfect scattering pattern is indicated by Moran's I value of 1.In contrast, a value of zero indicates a spatial pattern consistent with random chance, and a value of one announces a clustering pattern of perfect spatial autocorrelation.Let us consider the following hypotheses to be tested, The data from each of the 64 districts is independent and not influenced by the data from neighboring districts, suggesting there is no autocorrelation of DF rates between neighboring sites.A random pattern exists.However, the significance of any observed grouping depends on the p-value.Extreme clustering occurs when z-scores have large absolute values; nevertheless, the p value determines the statistical significance of this grouping.When both the p value and the z-score are below the significance threshold (0.05), the null hypothesis is rejected.As a result, we can infer the existence of clustering. 42High p values and small z-scores on the other hand, are consistent with accepting the null hypothesis.

| Local Moran's I
4][45] When comparing two districts to their neighbors, one of the most used measures of how similar they are to one another is the local Moran's I. 38 Where, in this research, p i determines the dispersion of district i's prevalence rate relative to the mean and p j determines the weight of district i's neighbors in the statistic, adjusted for the number of neighbors.

| Geary C
Geary's Cis a spatial statistical model for assessing the degree to which a data set is spatially auto-correlated and spatially dependent. 38Using a new method to measure spatial patterns, it is comparable to Local Moran's Iand Moran's Imodels.As a measure of spatial autocorrelation, Geary's Ctries to determine if there is a connection between separate instances of the same event. 47cause the connection is multidimensional and bidirectional, understanding spatial autocorrelation is more challenging than understanding traditional autocorrelation.In this research, the functional form of Geary C, stated in, 47 can be expressed in the following Equation (3):

| Local Getis Ord G
A variable can be changed into an independent variable by decreasing the spatial dependency in a spatially autocorrelated variable.After partitioning the original variable into two parts, filtered non spatial and residual spatial variables emerge.Determination of a suitable distance d is required in the transformation procedure within which neighborhood area units are dependent spatially. 48One process for identifying d includes evaluating the G i statistic at increasing distances till no spatial autocorrelation remains. 49From the rise of the observation, both statistics value G i and d increase, thus indicating the presence of spatial autocorrelation.The filtered observation, which is denoted by x* i is as follows: where,x i is the original observation, the formula for W i involves summing up all the geographic connections w ij , where each link for I and each j within d of i i j ( ≠ ) is usually weighted as one.n is the number of observations, G d ( ) i refers to the spatial autocorrelation statistic developed by: 49

| Spatial regression models
Spatial regression is a branch of regression analysis that incorporates geographical information.The presence of spatial dependency among a set of data indicates the presence of an autoregressive process.
According to the Poisson-Gamma model, the observations are presumed to be independent.When spatial data are correlated, it does not consider the spatial correlation between risk in surrounding districts and does not allow for straightforward adjustment for spatial factors. 39dels such as CAR, PLN, COV, and BYM2 were therefore considered.

| PLN model
The dengue incidence in the districts of Bangladesh is a mixture of

| CAR model
The CAR model considers the spatial dependency among neighboring districts, which is crucial in understanding the spread of Dengue infections.The CAR model incorporates a district-specific random effect component to account for the ensuing variation by taking into account factors that vary consistently over area. 39The model was first presented in an empirical Bayes context by, 52 and it was further expanded in a purely Bayesian environment by. 44The model can be written as: where: In this research, α determines the overall level of prevalence rate, and u i represents specific random effects of each district.By introducing this spatially structured random effects, it captures the tendency for Dengue cases to cluster because of their close proximity to one another.In other words, this model employs a spatial correlation structure to calculate an area's risk level relative to its neighbors. 52An intrinsic CAR model implies that the linked heterogeneity terms will work deterministically under the assumption of a normal distribution where the mean and variance are weighted by the averages and variances of the neighboring areas, 53 that is: where mean u ̅ i determines the average spatial random effects of neighbors and σ u 2 is the variance parameter with precision τ =

| COV model
The Bayesian implementation. 44It can be expressed as: It employs a structure of spatial correlation to calculate an area's prevalence rate with respect to its neighbors.It is believed that this follows a normal distribution.

| BYM2 model
According to, 55  ( ) where u* i resembles the scaled structured effect and and ϕ τy for u* with independent interpretability.The Dean model was introduced by scaling the neighborhood matrix integrating a new method termed penalized complexity (PC) priors, which assign priors to the hyperparameters. 55 priors can be applied to mixing and precision parameters in the BYM2 model.

| Deviance information criterion (DIC)
The DIC and a related measure p D , which counts the number of most essential model parameters, are used to compare different models. 56 a Bayesian framework, it is especially important to understand how to define the effective number of parameters when dealing with complex models.Statistical significance is shown where, DIC difference > 5, but a DIC difference < 5 does not disprove the model with the higher DIC.Due to its reliance on Markov chain Monte Carlo (MCMC) results, DIC is vulnerable to sampling errors. 57Let the vector of parameters associated with y be, then use the model and prior independence to show that DIC is additive.Then The definition of posterior deviance is as follows, where D determines the posterior expected value of the deviance function: and the Bayesian deviation, respectively.
Under priors and independent models, it is found . 53When D is small, the model fits the data quite well.If the p D difference between the two models was small, then the simpler model was adopted. 52

| Data analysis
In 2022, Chattogram district had the highest number of DF cases, with a total of 15,752, making it a notable hotspot in Figure 2.
Chattogram, the second-largest city in Bangladesh after Dhaka, located in south-eastern part of Bangladesh map, is seeing significant population expansion due to its prosperous ports, economic prospects, robust infrastructure, educational institutions, and modern amenities.Cox's Bazar and Barishalwere identified as the most affected districts in the country.On the other hand, the Gaibandha and Kurigram districts have a lower number of DF cases.Less densely populated regions, such as the hilly Bandarban, had lower reported viral cases, emphasizing the relationship between population density and disease transmission.Most cases of DF are found in tropical and subtropical locations, particularly in Southeast Asia, the western Pacific islands, Latin America, and Africa.As the primary vector for the transmission of DF, A. aegypti 58 prefers habitats with SARKER ET AL.
| 7 of 20 temperatures ranging from 26°C to 30°C and relative humidity levels between 70 and 80 percent.These conditions provide perfect breeding grounds 59 and sufficient food supplies 60 for the population to grow.
The frequency of DF varies across districts in Bangladesh, with Khulna district in the south-west having the highest prevalence rate despite its smaller population compared to Chattogram (see Figure 2).The variation is because there are more affected individuals in Chattogram.Khulna has a higher calculated prevalence rate than Chattogram, despite its smaller population, due to its potential impact on its larger population.DF typically peaks annually from July to November, following the rainy season, with varying degrees of severity across regions.Gaibandha, located in the northern region, has the lowest rates, with Barguna and Pirojpur in the southwest following closely behind in second and third place in frequency.
Barguna, with its smaller population and slower growth rate, has a more significant impact than Cox's Bazar.Pirojpur has a higher dengue prevalence rate than Barishal, despite Barishal having a lower rate due to its larger population.
Table 1 shows the prevalence rate assessment of DF using the Moran's I statistic, which resulted in a positive value of 0.464, suggesting spatial autocorrelation of DF rates among districts.
According to the findings of the statistical study, the null hypothesis is not supported because the p value is below 0.005 and the z-value     approval from regulators in multiple countries. 63One potential solution involves the creation of a vaccine. 58DENVax and TV003/ TV005 are two additional live-attenuated vaccination options, but their costs make them unaffordable for most individuals.The total expense for the suggested three doses of Dengvaxia in Indonesia is around US $207. 63If the cost of existing mosquito repellent creams rises tenfold, we can anticipate an even more significant increase in the price of Dengvaxia.The next potential outbreak caused by mosquitoes remains unidentified.Instead of focusing on dengue or chikungunya, our efforts should be directed toward minimizing the chances of mosquito bites. 64aling with the A. aegypti and A. albopictus mosquitoes can be quite challenging due to their ability to breed in various water sources, requiring urgent attention in all regions of Bangladesh.
Utilizing aerial pesticides as a proactive approach can help decrease the number of adult mosquitoes.Using residual pesticides indoors may have its benefits, but it may not be practical in crowded areas.
For this investigation, we focused solely on one response variable and did not consider other factors apart from population density in the study location.By including more potential risk factors in the model, we can achieve more widely applicable results.In future investigations, we plan to incorporate Bayesian hierarchical spatial modeling and additional factors such as climatic variables, demographic variables, vector characteristics, the latent period of infections, breeding sites, and more.The findings of this research will have led to uncovered additional valuable insights.

| LIMITATIONS
Every study has its limits, and our study is no exception.This analysis must account for the uncertainty in estimating the unobserved population sizes in 2022, which could impact the results, but it is challenging to address.Calculating it would have enhanced the accuracy of our investigation.Due to time constraints and lack of data, we could not include any risk factors.Incorporating risk factors into our analysis would enhance its robustness and precision.We aim to incorporate risk variables in future studies.
no studies have examined the geographical dependence of dengue cases throughout Bangladesh's 64 districts.Most established statistical methods assume initially that the data are uncorrelated.Traditional approaches are ineffective or irrelevant because they rely on assumptions of independence and homogeneity (stationarity), both of which are violated by cluster patterns.

H 1 :
The data acquired in each of the 64 districts demonstrate a nonrandom pattern or structure, as evidenced by the positive spatial autocorrelation of DF rates between neighboring districts.
) where x determines the variable of interest and ω ij is a quantification of the spatial weight of two districts i and j.The value of Geary C ranges within [0, 2].If the value falls within 0 C ≤ < 1, then it indicates positive autocorrelation among the districts.In addition, if it falls within C≥ 1, it indicates little spatial autocorrelation.On the contrary, if it falls within 1 C ≤ < 2, then it indicates the presence of negative autocorrelation between the districts.

2 2 i with precision τ = v σ 2 1 v 2 .
low and high.Taking into account this situation of this overdispersion we also incorporated the PLN model here.So, even in areas where Dengue cases are rare or frequent, this model can understand the differences in infection rates among those places.It's like having a magnifying glass to see the small details.The PLN model is an alternative to the Poisson-Gamma model.The prevalence rate, denoted by θ i , is related to a linear predictor with a random effects component, v i , that follows a normal distribution.52It can be expressed in terms of the log-normal model which possesses the following formula: generates the district-specific random effects and α determines the total level of the prevalence rate, which captures the additional Poisson variability in the log-prevalence rate of DF in the region i.In the Poisson-Gamma model, Gamma a b θ ~(, ) i where e ~Lognormal (0, σ ) v v Here, the variance of random effect (σ v 2 ) reflects the amount of extra Poisson variation in the data.

σ u 2
controls the strength of spatial similarity.To implement the CAR model we use gamma prior for σ u 2 .

.
The multiplicative conditional and marginal distributions of y contribute additively to Equation 4 in Bayesian deviation, resulting in the extreme value of y DIC DIC = ∏ k k k =1

is above 5 .
Figure 3 using a density plot.This plot is skewed to the right, which supports the presence of positive spatial autocorrelation.

F
I G U R E 2 (A) District-wise dengue affected cases; and (B) District-wise dengue prevalence rate.T A B L E 1 Descriptive statistic of Moran's I and Geary C calculated under randomization.influence of spatial lag and the spatial weights of the districts that are close to one another, the LISA cluster map displays the most important districts with weighted spatial homogeneity at a 90% confidence interval (see Figure 4).This widely used choropleth map categorizes locations having a high value of the local Moran's I statistic from Equation 2 according to the nature of the spatial correlation between them.The spatial clusters with high-high intensity are depicted in red, while those with low-low intensity are shown in blue.Low-High spatial outliers are depicted in light blue, whereas High-Low ones are depicted in light red.The map in Figure 4 illustrates that several districts in Bangladesh-Bandarban, Cox's Bazar, Narail, Bagerhat, Khulna, Pirojpur, Jhalokathi, Barguna, Barishal, Patuakhali, Madaripur, Gopalganj-are part of a significant cluster with a high−high intensity of dengue rate.The article highlights the significant occurrence of DENV in these districts and the prevalence rate of other vector-borne diseases, suggesting that the surrounding areas pose a considerable risk.Conversely, Panchagarh, Thakurgaon, Dinajpur, Nilphamari, Lalmonirhat, Kurigram, Jamalpur, Bagura, Joypurhat, Rangpur, Gaibandha, Sylhet, Sunamganj, Moulvibazar, Habiganj, and Kishoreganj are part of a significant spatial cluster with Low-Low intensity of dengue risk.The incidence of DF in these districts is low, similar to the surrounding areas.Despite having five times the population of Khulna, Chattogram and Khulna are both considered high-risk zones.The population of Khulna does not align with the prevalence rate.Therefore, the city's calculated prevalence rate holds more weight than Chattogram's.Furthermore, the Low-High spatial outliers consist of the three districts in Bangladesh: Satkhira, Shariatpur, and Rangamati.In these three districts, the prevalence rate is relatively low compared to the surrounding areas.The Local G coefficient takes an alternative approach from the Local Moran's I coefficient, which considers spatial outliers.Notably, in the Local G coefficient map, the Low-High and High-Low clusters found in the LISA map are reclassified as High and Low clusters, respectively.This difference stems from the underlying assumption of the G i index: spatial aggregation.Using concentrations of either low or high values, the G i index finds "hot spots" that provide low and high values for the index, respectively.Instead of capturing spatial variation in clusters like High-High, Low-Low, Low-High, and High-Low, G i cluster maps are made to show the geographic aggregation of High and Low zones. 49In Figure 5, our analysis demonstrates high prevalence rate associated with dengue in specific geographic areas.These areas encompass Bandarban, Cox's Bazar, Narail, Bagerhat, Khulna, Pirojpur, Jhalokathi, Barguna, Barishal, Patuakhali, Madaripur, Gopalganj, Satkhira, Shariatpur, and Rangamati.On the other hand, districts such as Panchagarh, Thakurgaon, Dinajpur, Nilphamari, Lalmonirhat, Kurigram, Jamalpur, Bagura, Joypurhat, Rangpur, Gaibandha, Sylhet, Sunamganj, Moulvibazar, Habiganj, and Kishoreganj exhibit clusters denoting a low prevalence rate for dengue.Using the likelihood and prior, the posterior distribution of Possion-Gamma, PLN, CAR, and COV have been fitted and the posterior estimates of the distributions have been calculated is summarized in Table 2.A dependable interval indicates that the actual value is likely to fall between the lower and upper limits of the interval.The lowered σ ˆu 2 value in the COV model compared to CAR indicates that the model more effectively captures the variations within each district by considering the associations among observations within each district.The τ ˆu 2 value for the CAR model is 18.27, indicating moderate precision and suggesting some variability in the spatial patterns.On the other hand, the value of 5766 for the same F I G U R E 3 Density plot of global Moran's I. LISA, Local Indicators of Spatial Autocorrelation.F I G U R E 4 LISA cluster map for prevalence rate.LISA, Local Indicators of Spatial Autocorrelation.F I G U R E 5 Getis Ord Gi map for prevalence rate.parameter in the COV model indicates that the spatial patterns or structures captured are highly consistent and well-defined, with minimal variability.In addition, the τ ˆv 2 value for the COV model is high at 7882, suggesting that the nonspatial random effects are consistent and well-defined, significantly contributing to explaining the variability in the outcome.When random factors are not considered, the marginal deviation from the model in the BYM2 model, 1 τˆγ , is 0.163, indicating that the model's efficacy in describing data patterns is enhanced by the addition of random effects.Thus, the random effects improve the model by capturing a portion of the unexplained variations in the data.The values for the DIC of five models (two nonspatial and three spatial) can be found in Table 2.A DIC discrepancy of more than 10 is a reason for favoring the model with a lower DIC value.While the DIC values of the COV model and BYM2 are close, the difference between them exceeds 10, making the lowest value of the BYM2 model acceptable.Other measuring factors, such as D ¯and p D are relatively small.Hence, compared to other models, the BYM2 performed exceptionally well and explained the spatial heterogeneity of dengue infections across 64 districts.

Figure 6 3 |
Figure 6 does not exhibit significant visual distinctions between the BYM2 model and the COV model.However, when considering DIC, the BYM2 model demonstrates a superior fit.The BYM2 model not only exhibits the lowest residual values but also successfully captures nearly all districts depicted on the thematic map because nearly all districts share the same color.There is an absence of any noticeable Barguna and Pirojpur in southwest Bangladesh pose a notable risk, though less severe than Khulna in the same geographical area.The government should share information and ensure that protective gear is readily available.Preventative measures should be within the financial reach of the general population.Reducing the mosquito population is crucial in combating diseases transmitted by mosquitoes.These measures mainly aim to get rid of places where adult mosquitoes and their larvae can breed.62Despite its constraints, the first licensed vaccine for dengue, Dengvaxia (Sanofi), received F I G U R E 6 Residual plots (A) Poisson-Lognormal model; (B) Conditional Autoregressive model; (C) Convolution model; (D) BYM2 model.

Figures| 15 of 20 F
Figures A6-A10 illustrate that autocorrelation diminishes rapidly and estimators blend effectively before examining any specific case.Thus, there is no indication of autocorrelation.Stationarity and excellent mixing in the trace plots are highly sought-after qualities.The path needs to stay within the posterior distribution to be considered stationary.More specifically, each trace groups together around one incredibly stable pattern.Stationarity is illustrated in Figures A11-A15.Second, achieving a good mix involves ensuring that no two samples within a parameter are statistically indistinguishable.As the trace moves through the posterior distribution, it meanders along various pathways.Trace plots from experiments highlight the second characteristic that helps clarify statistical significance.Both the red and blue stores utilized these options.
52mma model, a mixed model with gamma random effects for each area.52Thismodel accounts for over-dispersion in count data, which is common in epidemiological studies like Dengue infections.Dengue case counts are assumed to be random throughout each district in this model and it follows a Poisson distribution with mean e θ 50,512.9 | Poisson-Gamma model An alternative interpretation of the negative binomial distribution (Poisson model for modeling additional variation) is the Poisson- 54d an uncorrelated heterogeneity component v i , where u i models the effects that vary in a predictable way between locations and v i represent effects that vary randomly across locations.Clayton and Kaldor similarly proposed this model in an empirical Bayes setting54and Besag et al. developed it in a fully 52atial impact but also how the infection spreads over subsequent periods.This is crucial in evaluating the spatial dynamics of Dengue transmission and the potential for outbreaks to spill over into neighboring areas.To account for spatial autocorrelation, convolutional models incorporate a random-effects term, similar to the one used to account for over-dispersion.52Itdissects random effects of district-level into a correlated heterogeneity component u i Summary statistics of Poisson-Gamma, PLN, CAR, COV, and BYM2 models.
61e results of this study highlight an increased risk in densely populated districts such as Chattogram, which has the highest number of cases identified.Factors such as overpopulation, rapid T A B L E 2 Note: Bold values are used to highlight the best model.Abbreviations: CAR, Conditional Autoregressive; COV, Convolution; PLN, Poisson-Lognormal.| 11 of 20 spread, lack of security, and a lack of preventative measures are assumed to increase the level of risk.A decreased prevalence rate will inevitably lead to fewer cases since the number of infected instances is directly proportional to the prevalence rate.Khulna has the highest prevalence rate compared to other cities in Bangladesh.Due to the combination of heavy rains, waterlogging, flooding, increased temperatures, and unpredictable changes in the district's usual seasons, the conditions in Khulna have become conducive for a dengue outbreak, worsening the situation.61Evidenceindicates that